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Anti-tuition fee campaigners have an uphill battle to convince enough Liberal Democrats to rebel in a parliamentary vote to defeat any proposal to hike tuition fees, a survey of backbench MPs shows.

Fewer than 10 Lib Dem MPs have said publicly that they will vote against a rise after Vince Cable, the business secretary, said the party's opposition to fees was "no longer feasible" in today's fiscal conditions.

More than 40 Lib Dems would probably need to vote against the government rather than abstain, as the coalition agreement allows them to do, if a motion to hike fees were to fail. Given that 16 of the party's 57 MPs are in the government - and therefore less likely to rebel - the figures are stacked against the National Union of Students, which is leading the campaign against a rise in fees.

A survey by Times Higher Education of Lib Dem backbenchers shows that most are still undecided.

About half the backbenchers responded when asked how they would vote if tuition fees in excess of £5,000 were proposed for home students. Eight say they will vote against, 13 are undecided and one plans to vote in support.

Among those who have stated publicly that they plan to rebel are Sir Menzies Campbell, Julian Huppert, John Leech, Greg Mulholland and Bob Russell.

Mr Huppert, the MP for Cambridge, said he hoped Mr Cable would force progressive elements into the government's proposals.

But he added: "I think what Vince is pushing is more than the Tories or Labour would do on their own, but it is not enough for me."

The situation could be made more complicated by the choices of Conservative and Labour MPs and whether fringe parties such as the Scottish National Party, Plaid Cymru and those from Northern Ireland vote on the proposals.

Three Tory MPs signed the NUS pre-election pledge to vote against higher fees, while Labour is expected to whip its MPs into opposing the government. However, most Labour MPs failed to sign the pledge and some could rebel by abstaining or supporting the government.

Plaid Cymru said its MPs would take part in any vote proposing higher tuition fees in England due to the potential knock-on effect for Welsh universities. The SNP, which traditionally abstains from votes affecting England only, said it may participate.

The vote is likely to take place against the bizarre backdrop of the Lib Dems officially being opposed to fees after the party's Federal Policy Committee confirmed last week that it remained committed to phasing them out.